QMT181 Uitm Dungun 2014

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CHAPTER 2 : DATA PRESENTATION
2.1 ORGANISING AND GRAPHING QUALITATIVE DATA
Qualitative data can be classified into categories or classes. They can best be presented in the form of frequency distribution, bar chart, pie chart and contingency table.
a) Frequency distribution
There are many forms of tables available such as :
i) One-way table - the simplest form of table that describes information concerning
a single variable.
Example 1:
The number of contractors in State EMAS.
Class
Number of contractors
A
7
B
17
C
23
D
35
E
40
ii) Two-way table or contingency table – summarizes information concerning two
variables.
Example 2:
The number of contractors in State EMAS according to District.
District
Class Category
A
B
C
D
E
X
3
4
8
10
15
Y
2
6
10
16
13
Z
2
7
5
9
12
b) Bar Charts
Bar charts are very often used in newspapers and magazines to convey information.
A bar chart is one that uses the length of horizontal bars or vertical columns to represent quantities or percentages.
i) Simple Bar Chart
A simple bar chart is one in which the bars represent one unit quantity or variable only. The length of the bar indicates quantities or percentages.
Example 3
Refer to table example 1

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The number of contractors in state EMAS
0
5
10
15
20
25
30
35
40
45
A B C D E
Class
Frequency
ii) Multiple Bar Chart (Cluster bar chart)
Example 4
Refer to table example 2
The number of contractors in state EMAS according to district
0
2
4
6
8
10
12
14
16
18
A B C D E
Class
Frequency
X
Y
Z
iii) Component Bar Charts (Stacked bar chart)
A component bar chart is one in which some of the bars are stacked on top of each other. This
type of bar chart is often used when various totals are also to be compared.
Example 5
Refer to table example 2
The number of contractors in state EMAS according to district
0
5
10
15
20
25
30
35
40
45
A B C D E
Class
Frequency
Z
Y
X

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iv) Percentage component bar charts
Example 6
Refer to table example 2
Convert the values to percentage
A B C D E
X 42.9 23.5 34.8 28.6 37.5
Y 28.6 35.3 43.5 45.7 32.5
Z 28.6 41.2 21.7 25.7 30.0
The number of contractors in state EMAS according to district
0.0
20.0
40.0
60.0
80.0
100.0
120.0
A B C D E
Class
Percentage
Z
Y
X
c) Pie Charts
Example 7
Refer to table example 1
The number of contractors in state EMAS
A
6%
B
14%
C
19%
D
29%
E
32%

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2.2 ORGANISING AND GRAPHING QUANTITATIVE DATA
Terminologies for a Frequency Distribution
a) Class limits - the end values of a class interval. The value on the left is the lower class limit and the value on the right is the upper class limit.
b) Class Boundary - a value that falls midway between the upper limit of one class and the lower limit of the next one.
c) Class midpoint - the middle value of a class interval. Can be determined by averaging either the class limits or the class boundaries.
d) Cumulative frequency - is determined by summing the frequencies for the class and all prior classes.
Example 8:
A frequency distribution table showing the price of houses at Bandar Teronoh is shown below:
Cost (RM’000)
Number of houses
Class boundary
Midpoint
Cumulative frequency
110-119
9
109.5-119.5
114.5
9
120-129
12
119.5-129.5
124.5
21
130-139
16
129.5-139.5
134.5
37
140-149
11
139.5-149.5
144.5
48
150-159
8
149.5-159.5
154.5
56
160-169
4
159.5-169.5
164.5
60
Amount of Steel (tones)
Number of Buildings
Class boundary
Midpoint
Cumulative frequency
4 and less than 6
1
4 - 6
5
1
6 and less than 8
4
6 – 8
7
5
8 and less than 10
5
8 – 10
9
10
10 and less than 12
8
10 – 12
11
18
12 and less than 14
5
12 – 14
13
23
14 and less than 16
2
14 – 16
15
25
b) Histogram
c) Frequency Polygon
d) a less than ogives

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e) Stem-and-Leaf Displays
 A statistical technique to present a set of data.
 Each numerical value is divided into two parts.
 The leading digit(s) becomes the stem and the trailing digit the leaf.
 The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis.
Example 9 ;
Number of Advertising Spots Purchased by Members of the Greater Buffalo Automobile Dealers Association
96 93 88 117 127 95 113 96 108 94 148 156
139 142 94 107 125 155 155 103 112 127 117 120
112 135 132 111 125 104 106 139 134 119 97 89
118 136 125 143 120 103 113 124 138
Solution;
The smallest number is 88, so we will make the first stem value 8.
The largest number is 156, so we will have the stem values begin at 8 and continue to 15.
Organizing all the data, the stem-and-leaf chart looks as follows
Stem
Leaf
8
9
10
11
12
13
14
15
8 9
3 4 4 5 6 6 7
3 3 4 6 7 8
1 2 2 3 3 7 7 8 9
0 0 4 5 5 5 7 7
2 4 5 6 8 9 9
2 3 8
5 5 6
You can convert the stem-and-leaf chart to frequency table, looks as follows.
(if you want to draw a graph)
Class
Frequency
80 – 89
90 – 99
100 – 109
110 – 119
120 – 129
130 – 139
140 – 149
150 - 159
2
7
6
9
8
7
3
3